The carrots we buy from a supermarkets spoil very fast, albeit giving many consumers a false sense of preservability due to their structural rigidity. The answer extends to many other vegetables many of us eat:

Larsinio (2006)- wikimedia, public domain, DOR 27/09/2012

The question is, why do well aerated carrots spoil in the matter of days, at room temperature?

Remember that tubers are designed for a relatively anaerobic environment. My guess is that what you are seeing is related to that. Oxidation perhaps? Aerobic bacteria gone wild?
–
terdonSep 27 '12 at 11:18

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I think carrot keeps long time in refrigerator. Why store it at room temp when optimal storing condition is refrigerator ?
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AndreiSep 27 '12 at 20:01

@Andrei Initially I wanted to explain that in the post as well and include storage conditions. But I consider it best to just ask one question at a time. Regardless, did you have consistently success w. long-term fridge storage?
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Lo SauerSep 28 '12 at 5:35

can you reference your declaration that carrots spoil fast please since I also think that it depends on a lot of factors like where it was grown, the kind of fertilizers used etc
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The Last WordJun 4 '14 at 10:41

1 Answer
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First we will take a look at the lines of resistance of a carrot. There are three

The skin - The first line of resistance is the outer membrane or skin of the carrot and chemical compounds that are normally present
there. Two antifungal polyacetylenes, falcarinol and falcarindiol, and
an isocoumarin, 6-methoxymellein, are present in small amounts in a
normal carrot and present the first barrier in undamaged carrots.

Post Harvest - If during harvest or post harvest handling this barrier is broken, the surface is punctured, scraped or sliced,
microorganisms may begin to grow. The carrot at this point begins a
wound healing process by accumulating suberin, a complex
polysaccharide, at the wound site. Along with suberin, lignin is also
accumulated. Suberisation is complete within 48 hours after wounding,
and lignification is complete within 168 hours of wounding..

Phytoalexin barrier - The last and most important line of resistance is the phytoalexin barrier. Phytoalexins are chemicals
produced by plants that impart disease resistance in response to
mechanical injury, physiological stimuli or infection. Scopoletin, a
coumarin,and para-hydroxy benzoic acid, a phenol, are apparently early
arrivals on the scene but later disappear (reference).

There are three enemies of carrot storage: wilt, re-growth and rot.

Some reasons for carrots rotting faster:

Many fruits and vegetables start to produce ethylene gas when they start to ripen. Some foods are extremely sensitive to ethylene gas which makes them rot faster (reference). I am guessing that you keep different vegetables close together. Maybe if you stored carrots separately, it might make them last a bit longer.

Major post-harvest losses in carrots are due to Sclerotinia rot,
Botrytis rot, Bacterial soft rot (Erwinia) and Sour rot (Geotrichum).
Of these, Sclerotinia rot is the most prevalent.The Sclerotinia fungus
infects the carrot roots in the field through the crown. During
storage, the Sclerotinia fungus produces a white, cottony mycelium
which covers the roots. Infected roots are usually soft and watery (reference).

There would definitely be more reasons but I am guessing that these are the major contributors to it rotting faster.